SQU Journal for Science, 2016, 21(2), 89-101 

© 2016 Sultan Qaboos University  

89 

 

Computational Study of Geometry, 
Solvation Free Energy, Dipole Moment, 
Polarizability, Hyperpolarizability and 
Molecular Properties of 2-Methylimidazole 

Mohammad Firoz Khan1, Ridwan Bin Rashid2, Shahidul M. Islam3* and                      
Mohammad A. Rashid4* 

1Computational Laboratory, Department of Pharmacy, State University of Bangladesh, Dhaka- 
1205, Bangladesh; 2Department of Microbiology, University of Dhaka, Dhaka-1000, 
Bangladesh; 3Department of Chemistry, College of Science, Sultan Qaboos University, P.O. 
Box 33, AlKhoud, PC 123, Muscat, Sultanate of Oman; 4Department of Pharmaceutical 
Chemistry, University of Dhaka, Dhaka- 1000, Bangladesh. *Email: shahidul321@gmail.com; 
rashidma@du.ac.bd 
 

ABSTRACT: Ab initio calculations were carried out to study the geometry, solvation free energy, dipole moment, 

molecular electrostatic potential (MESP), Mulliken and Natural charge distribution, polarizability, 

hyperpolarizability, Natural Bond Orbital (NBO) energetic and different molecular properties like global reactivity 

descriptors (chemical hardness, softness, chemical potential, electronegativity, electrophilicity index) of 2-

methylimidazole. B3LYP/6-31G(d,p) level of theory was used to optimize the structure both in the gas phase and 

in solution. The solvation free energy, dipole moment and molecular properties were calculated by applying the 

Solvation Model on Density (SMD) in four solvent systems, namely water, dimethylsulfoxide (DMSO), n-octanol 

and chloroform. The computed bond distances, bond angles and dihedral angles of 2-methylimidazole agreed 

reasonably well with the experimental data except for C(2)-N(1), C(4)-C(5) and N(1)-H(7) bond lengths and N(1)-

C(5)-C(4) bond angle. The solvation free energy, dipole moment, polarizability, first order hyperpolarizability, 

chemical potential, electronegativity and electrophilicity index of 2-methylimidazole increased on going from non-

polar to polar solvents. Chemical hardness also increased with increasing polarity of the solvent and the opposite 

relation was found in the case of softness. These results provide better understanding of the stability and reactivity 

of 2-methylimidazole in different solvent systems. 

 

Keywords: 2-Methylimidazole; Solvation free energy; Dipole moment;Polarizability; Solvation model. 

ميثيل ايميدازول-2الدراسة النظرية للتركيب الهندسي، والطاقة الحرة لإلذابة، والعزم القطبي، واإلستقطاب، والخصائص الجزيئية لـ   

 محمد فيروز خان1، رضوان بن راشد2، شهيدول م. إسالم3* ومحمد أ. راشد4

تم تنفيذها لدراسة التركيب الهندسي والطاقة الحرة لإلذابة والعزم القطبي والطاقة الكهروستاتيكية الجزيئية وتوزيع مليكان  حسابات آب انيشيو :ستخلصم

 لليونة، الكمونوالطبيعي للشحنات واإلستقطاب وطاقة الربط المداري والخصائص الجزيئية المختلفة كاألوصاف التفاعلية الكونية ) الصالبة الكيميائية، ا

استخدم لتحسين التركيب في  B3LYP/6-31G(d,p). المستوى النظري ميثيل ايميدازول -2إلى  الكيميائي، السالبية الكهربائية، مؤشر األلفة الكهربائية(

 (SMD)الكثافة الحالة الغازية وفي المحلول. الطاقة الحرة لإلماهة، والعزم القطبي، والخصائص الجزيئية تم حسابها من خالل تطبيق نموذج اإلذابة على 

طول الروابط الكيميائية والزوايا المحسوبة  ، واألوكتانول، والكلورفورم.(DMSO)في نظام من أربعة مذيبات وهي الماء، وثنائي ميثيل السلفوكسيد 

والزاوية في  N(1)-H(7)و  C(2)-N(1), C(4)-C(5)ميثيل ايميدازول تتوافق بشكل معقول مع النتائج التجريبية ماعدا لطول الرابطة في -2للمركب 

N(1)-C(5)-C(4)،2والسالبية الكهربائية، ومؤشر األلفة الكهربائية للجزيء  . الطاقة الحرة لإلذابة، والعزم القطبي، واإلستقطاب، والكمون الكيميائي-

لنسبة للليونة. نتائج هذه ميثيل ايميدازول يزيد كلما اتجهنا من أقل المذيبات قطبية إلى أكثرها. الصالبة الكيميائية أيضا تزيد بزيادة قطبية المذيب والعكس با

 ميثيل ايميدازول في أنظمة مختلفة المذيبات. -2للجزيء الدراسة تساعد في فهم مدى الثبات والقدرة التفاعلية 

 

 ميثيل ايميدازول، الطاقة الحرة لإلذابة، العزم القطبي، اإلستقطاب، نموذج اإلذابة. -2: كلمات مفتاحية

 

mailto:shahidul321@gmail.com
mailto:rashidma@du.ac.bd


SHAHIDUL M. ISLAM ET AL 

90 

 

1. Introduction 

he 2-methylimidazole (Figure 1) is a nitrogen-containing heterocyclic organic compound. It is structurally related 

to imidazole with the chemical formula C4H6N2. It is a solid substance with high solubility in polar solvents. The 

2-methylimidazole is commonly used as a chemical intermediate in the production of pharmaceuticals, dyes and 

pigments, photographic and photothermographic chemicals, agricultural chemicals, and rubber [1]. It is formed by the 

ammoniation of sugars and considered a by-product of food and forage colored with caramel. 

The N-substituted derivatives of imidazole and of the 2-methylimidazole exhibit a wide range of pharmacological 

properties, such as antiparasitic [2], antifungal [3], and antimicrobial activities [4], which has made it a subject of 

interest to organic and medicinal chemists [5]. This compound was explored against E. coli, S. aureus and P. 

aureginosa for antibacterial activity [6]. Because of its wide presence and lack of carcinogenic information, the toxicity 

studies of this compound were carried out in rats and mice [7-9]. The 2-methylimidazole has also been detected in 

mainstream and side-stream cigarette smoke as a result of pyrolysis [10]. The length of the alkyl chain on the imidazole 

ring is very important for biological activity, i.e. 1-alkylimidazoles require a hydrocarbon chain of 12 carbons to 

exhibit antifungal and cytotoxic activity and 10 carbons for inhibition of microsomal oxidation [3,6,11]. The 

thermochemical investigation has revealed that the standard molar enthalpies of formation for crystalline and gas phase 

of 2-methylimidazole are 1.4 and 89.8 kJ/mol, respectively, and standard molar enthalpies of sublimation is 88.4 

kJ/mol [12]. 

  

Figure 1. Structure of 2-methyimidazole. 

 

Fewer computational and theoretical studies of 2-methylimidazole have previously been reported. Yu et al. 

reported the experimental and theoretical study of interactions between the diperoxovanadate complexes and histidine-

like ligands, namely imidazole, 2-methylimidazole, carnosine, 4-methylimidazole and histidine [13]. The reactivity 

(coordination capability) of the ligands were found in the order of imidazole >2-methylimidazole>carnosine ≈ 4-

methylimidazole >histidine. Theoretical study of the formation of complexes between CO2 and imidazole derivatives 

has also been reported [14]. The most stable complex between 2-methylimidazole and CO2 is formed due to the charge 

transfer from the ring of 2-methylimidazole to the CO2. The variation in solvent polarity and the type of solute-solvent 

interaction(s) can affect the calculated geometry, dipole moment, polarizability, hyperpolarizability and other 

molecular properties [15,16] due to variable interactions with the frontier molecular orbitals [15,17], and hence, can 

influence the stability and reactivity of the molecule. Density Functional Theory (DFT) calculations provide a greater 

detail of molecular characteristics and interactions which lead to a good understanding of molecular properties [18].  

In the present investigation, computational studies have been carried out to better understand geometry, solvation 

free energy, dipole moment, molecular electrostatic potential (MESP), charge distribution, polarizability, 

hyperpolarizability and global reactivity descriptor properties such as the chemical hardness, softness, chemical 

potential, electronegativity, electrophilicityindex of 2-methylimidazole in different solvent systems, which could 

potentially be helpful for the development of pharmaceutical and (bio)chemical products. 

2. Methodology 

Computational methods 

All calculations were conducted with the Gaussian 09 software package [19]. From previous work [20,21], it was 

found that geometries, solvation free energies, dipole moment and molecular properties of similar systems obtained 

using the B3LYP/6-31G(d,p) showed better agreement with experiments. Therefore, methylimidazole geometries were 

optimized at the B3LYP electronic structure method [22-24] using the 6-31G(d,p) basis set. Frequencies were 

calculated to ensure the absence of imaginary frequencies in the lowest energy state. The Solvation Model on Density 

T 

N
H

N

H3C



COMPUTATIONAL STUDY OF GEOMETRY 

91 

 

(SMD) [14] as implemented in Gaussian 09 was used for all calculations involving the solvents, Water, DMSO, n-

Octanol, and Chloroform. The SMD model is highly parameterized, uses the original polarizable continuum model 

(PCM), and the charge density of the solute molecule interacts with the dielectric medium of the solvent through 

surface tension at the solute-solvent boundary. All calculations involving solvation were performed using the 

optimized solution-phase structures. The free energy of solvation (∆G) is calculated from the difference in gas phase 

and solvent phase free energies of a molecule as represented below, ∆G = G(sol) - G(gas) where G(gas) is the gas 

phase free energy which is obtained as follows: 

G(gas) = Sum of electronic and thermal Free Energies (1) + Thermal correction to Gibbs Free Energy (2). 

(1) and (2) are readily obtained from the Gaussian output file. Similarly, G(sol) is also calculated from a solvent phase 
simulation of the same molecule. 

3. Results and discussion 

Equilibrium geometries 

The optimized geometrical parameters such as bond lengths, bond angles, and dihedral angles of 2-methyimidazole 

obtained by the B3LYP/6-31G (d,p) are listed in Tables 1 and 2. The computed bond distances and bond angles were 

also compared with the X-ray crystallographic data [5]. From the Tables, it has been found that the calculated bond 

distances, bond angles and dihedral angles agreed well with the experimental data, except for the C(2)-N(1), C(4)-C(5) 

and N(1)-H(7) bond lengths and the N(1)-C(5)-C(4) bond angle. The Mean Absolute Deviation (MAD) is used to 

calculate the differences between the computed and experimental geometrical parameters and the MAD values for 

bond distances, bond angles and dihedral angles are 0.030 Å, 0.6˚ and 0.4ᵒ, respectively. 

 

Table 1. Theoretical (gas phase) and experimental (X-ray diffraction) bond distances (Å) of 2-methylimidazole. 

Assignment 
Theoretical 

Bond distances (Å) 

Experimental [5] 

Bond distances (Å) 

C(2)-N(1) 1.372 1.347 

C(2)-N(3) 1.319 1.327 

C(4)-C(5) 1.370 1.356 

C(4)-N(3) 1.379 1.384 

C(5)-N(1) 1.382 1.370 

C(2)-C(6) 1.494 1.487 

C(4)-H(8) 1.081 - 

C(5)-H(9) 1.079 - 

N(1)-H(7) 1.008 0.870 

C(6)-H(10) 1.096 - 

C(6)-H(11) 1.096 - 

C(6)-H(12) 1.091 - 

MAD 0.030   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



SHAHIDUL M. ISLAM ET AL 

92 

 

Table 2. Theoretical (gas phase) and experimental (X-ray diffraction) bond angle (ᵒ) and dihedral angles (ᵒ) of 2-

methylimidazole. 

 

Assignment 

Theoretical 

Bond 

angle (ᵒ) 

Experimental [5] 

Bond 

angle (ᵒ) 

Assignment 

Theoretical 

Dihedral 

angles (ᵒ) 

Experimental [5] 

Dihedral 

angles (ᵒ) 

C(2)-N(1)-H(7) 126.3 - C(2)-N(1)-C(5)-C(4) 0.0 0.1 

C(2)-N(1)-C(5) 107.7 107.4 C(2)-N(1)-C(5)-H(9) -180.0 - 

H(7)-N(1)-C(5) 126.0 - H(7)-N(1)-C(5)-H(9) 0.0 - 

N(1)-C(5)-H(9) 122.2 - H(7)-N(1)-C(5)-C(4) 180.0 - 

N(1)-C(5)-C(4) 104.9 106.2 N(1)-C(5)-C(4)-N(3) 0.0 0.3 

N(1)-C(2)-C(6) 123.3 123.0 N(1)-C(5)-C(4)-H(8) 180.0 - 

H(9)-C(5)-C(4) 132.8 - H(9)-C(5)-C(4)-H(8) -0.1 - 

C(5)-C(4)-H(8) 127.9 - H(9)-C(5)-C(4)-N(3) 180.0 - 

C(5)-C(4)-N(3) 110.8 109.9 C(5)-C(4)-N(3)-C(2) 0.0 0.4 

H(8)-C(4)-N(3) 121.4 - H(8)-C(4)-N(3)-C(2) -180.0 - 

C(4)-N(3)-C(2) 105.8 105.0 C(4)-N(3)-C(2)-N(1) 0.0 -0.3 

N(3)-C(2)-N(1) 110.8 111.5 C(4)-N(3)-C(2)-C(6) 180.0 179.4 

N(3)-C(2)-C(6) 125.8 125.5 C(5)-N(1)-C(2)-C(6) -180.0 -179.2 

C(2)-C(6)-H(10) 112.0 - N(3)-C(2)-N(1)-C(5) 0.0 0.0 

C(2)-C(6)-H(11) 112.0 - N(3)-C(2)-N(1)-H(7) -180.0 - 

C(2)-C(6)-H(12) 
108.3 - 

N(3)-C(2)-C(6)-

H(10) 
119.4 - 

H(10)-C(6)-

H(11) 
107.7 - 

N(3)-C(2)-C(6)-

H(11) 
-119.5 - 

H(10)-C(6)-

H(12) 
108.3 - 

N(3)-C(2)-C(6)-

H(12) 
-0.1 - 

H(11)-C(6)-

H(12) 
108.3 - H(7)-N(1)-C(2)-C(6) 0.0 - 

MAD 0.6   
N(1)-C(2)-C(6)-

H(10) 
-60.6 - 

   

N(1)-C(2)-C(6)-

H(11) 
60.5 - 

   

N(1)-C(2)-C(6)-

H(12) 
179.9 - 

   

MAD 0.4   

 

Solvation free energy  

The most important properties of a chemical system (solute) with surrounding solvent can best be described by 

means of free energy variation [25]. The solvation free energies of 2-methylimidazole calculated with the SMD model 

[26] are summarized in Table 3. The solvation energies of methylimidazole in water, n-octanol, chloroform and DMSO 

are -33.36 kJ/mol, -33.76 kJ/mol, -36.01 kJ/mol and -38.09 kJ/mol, respectively. The highest solvation free energy is 

found in polar aprotic solvent (DMSO) followed by nonpolar (chloroform) and polar protic solvents (n-octanol and 

water). Therefore, the hydrogen bond plays an important role in the solvation of 2-methylimidazole.  

Dipole moment 

The dipole moment of 2-methylimidazole in different solvents is found to be higher than that of the gas phase. 

Table 4 presents the dipole moments computed in the gas phase and different solvents (water, DMSO, n-octanol and 

chloroform) at the B3LYP/6-31G(d,p) using SMD solvation model. The dipole moments are 3.6D, 4.6D, 4.8D, 5.0D, 

and 5.1D in the gas phase, chloroform, n-octanol, DMSO and water, respectively. Therefore, there is a gradual increase 

in dipole moment on going from a lower to higher dielectric constant of the solvent. In other words, the dipole moment 

increases with the increasing polarity of the solvent (Figure 2). 

 



COMPUTATIONAL STUDY OF GEOMETRY 

93 

 

Table 3.Solvation free energy (kJ/mol) of 2-methylimidazole in different solvents with SMD. 

Medium (dielectric 

constant) 

Solvation free 

energy (kJ/mol) 

Water (78.3) -33.36 

DMSO (46.8) -38.09 

n-Octanol (9.9) -33.76 

Chloroform (4.7) -36.01 

 

Table 4. Dipole moment (Debye, (D)) of 2-methylimidazole in gas phase and in different solvents using SMD. 

 

Medium 

(dielectric constant) 
Dipole Moment (D) 

Gas 3.6 

Water (78.3) 5.1 

DMSO (46.8) 5.0 

n-Octanol (9.9) 4.8 

Chloroform (4.7) 4.6 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2. Effect of solvent polarity on dipole moment (D) of 2-methylimidazole. 

 

 

 

 

 

 

 

 

4.3

4.4

4.5

4.6

4.7

4.8

4.9

5.0

5.1

5.2

Chloroform (4.7) n-Octanol (9.9) DMSO (46.8) Water (78.3)

D
ip

o
le

 M
o
m

e
n

t 
(D

)

Solvents (Dielectric constant)



SHAHIDUL M. ISLAM ET AL 

94 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3. Electrostatic potential contour of 2-methylimidazole. 

 

Molecular electrostatic potential (MESP) 

The Molecular electrostatic potential (MESP) represents the net electrostatic effect of a molecule which is 

generated from the total charge distribution in the molecule. The MESP correlates very well with the partial charges, 

electronegativity, dipole moments and chemical reactivity of the molecule [27-29]. In the case of chemical reactivity, 

the region of the molecule susceptible to electrophilic or nucleophilic attack can be identified by the total electron 

density surface mapped with the electrostatic potential. The MESP contour map of 2-methyimidazole calculated at the 

B3LYP/6-31G(d,p) is shown in Figure 3. The red (negative) and blue (positive) color regions in the MESP surface 

represent the regions susceptible to the attack of electrophiles and nucleophiles, respectively. The map reveals that the 

most possible sites for nucleophilic attack are C2 and H7 and electrophilic attack are N1 and C4. 

Mulliken and Natural population analysis 

The Mulliken population analysis (MPA) and Natural population analysis (NPA) show the simplest picture of 

charge distribution. The Mulliken and Natural charges present net atomic charges in the molecule; while electrostatic 

potentials are generated by the electric field of internal charge distribution. Thus, in the reactivity studies, population 

analysis (MPA or NPA) and MESP are complementary tools, and correlation between the schemes is expected [30]. In 

this study, both MPA and NPA have been carried out to clearly understand the charge distribution among the atoms in 

2-methylimidazole. NPA is less dependent on the choice of basis set compared to the original MPA. Atomic charges 

obtained from MPA and NPA are found to be consistent with each other (Table 5). However, according to MPA, 

among all the carbon atoms only C(6) has negative charge, while in the case of NPA the C(6) along with C(4) and C(5) 

possess negative charges. The presence of two nitrogen atoms N(1) and N(3) imposes large positive charges on the 

C(2) atom. The MPA and NPA show that all the hydrogen and nitrogen atoms have positive and negative charges, 

respectively. Among all the H atoms, the H(7) possesses the highest positive charge. This shows that the charge 

distribution and the MESP information are concordant. 

Polarizability and First order Hyperpolarizability 

Polarizability is the measure of distortion of a molecule in an electric field. It is a tensor and can be represented in 

a 3 × 3 real symmetric matrix i.e. the off-diagonal elements are equal. The polarizability (α) was calculated using the 

following equation: 

𝛼 =  
1

3
 (𝛼𝑥𝑥 + 𝛼𝑦𝑦 + 𝛼𝑧𝑧 )                                                       (1) 

The quantities αxx, αyy and αzz are known as the principal values of the polarizability tensor. This property measures the 

strength of molecular interactions (e.g., long-range intermolecular induction, dispersion forces, etc.), the cross sections 

of different scattering and collision processes, and the optical properties of a system [17]. The calculated polarizability 

of 2-methylimidazole in different solvents is presented in Table 6, which shows that polarizability (αtot) of 2-

methylimidazole in these solvents ranged from 60.81 to 66.20 a.u. The plot of polarizability vs. solvent is shown in 

Figure 4. It is clear from the Figure that the polarizability gradually increases on going from lower to higher dielectric 

constant. 



COMPUTATIONAL STUDY OF GEOMETRY 

95 

 

Table 5. Atomic charges of 2-methylimidazole obtained from Mulliken population analysis (MPA) and Natural 

population analysis (NPA). 

 

Atom 

B3LYP/6-31G(d,p) 

MPA NPA 

N(1) -0.517 -0.579 

C(2) 0.451 0.378 

N(3) -0.474 -0.502 

C(4) 0.022 -0.104 

C(5) 0.064 -0.119 

C(6) -0.384 -0.735 

H(7) 0.260 0.435 

H(8) 0.085 0.232 

H(9) 0.103 0.236 

H(10) 0.120 0.244 

H(11) 0.120 0.244 

H(12) 0.150 0.271 

 

 

The first order hyperpolarizability (β) is the measure of the nonlinear optical activity which can be of different 

types such as βvec (β vector), β|| (β parallel) and βtot (β total). It is a third rank tensor that can be described by a 3 × 3 × 3 

matrix. The Kleinman symmetry enables the reduction of the 27 components of 3D matrix into 10 components [31]. 

GAUSSIAN provides 10 components of this matrix as βxxx, βyxx, βxyy, βyyy, βxxz, βxyz, βyyz, βxxz, βyzz, βzzz, respectively, 

from which all x, y and z components of β can be calculated. The hyperpolarizability (βtot) can be calculated using the 

following equation: 

𝛽𝑡𝑜𝑡 =  (𝛽𝑥
2 + 𝛽𝑦

2 + 𝛽𝑧
2)

1
2⁄                                                      (2) 

Where, 

 βx = βxxx + βxyy + βxzz 

 βy = βyyy + βxxy + βyzz 
βz = βzzz + βxxz + βyyz 

 

 

 

 

 

 

 

 

 

 

 

Figure 4. Effect of solvent polarity on polarizability of 2-methylimidazole. 

 

23.50

24.00

24.50

25.00

25.50

26.00

26.50

27.00

27.50

28.00

28.50

Water (78.3) DMSO (46.8) n-Octanol (9.9) Chloroform (4.7)

a
.u

.

Solvents (Dielectric constant)



SHAHIDUL M. ISLAM ET AL 

96 

 

 

 

 

 

 

 

 

 

 

Figure 5. Effect of solvent polarity on first order hyperpolarizability of 2-methylimidazole. 

 

The βtot for different solvents has been listed in Table 6, which shows that the hyperpolarizability in different solvents 

ranges from 24.24 to 28.22 a.u. Moreover, the hyperpolarizability increases on going from lower to higher dielectric 

constant i.e. from non-polar to polar solvents (Figure 5). 

Table 6. Effect of solvent polarity on polarizability (a.u.) and first order hyperpolarizability (a.u.). 

 

Medium 

(dielectric constant) 
αxx αyy αzz αtot βx βy βz βtot 

Gas Phase 67.01 54.00 27.57 49.53 1.33 19.57 0.00 19.62 

Water (78.3) 88.04 74.91 35.67 66.20 -0.09 28.22 0.00 28.22 

DMSO (46.8) 87.91 74.58 35.52 66.00 0.03 28.03 0.00 28.03 

n-Octanol (9.9) 85.16 71.46 34.17 63.60 -0.16 26.74 0.00 26.74 

Chloroform (4.7) 81.88 67.87 32.68 60.81 -0.37 25.24 0.00 25.24 

 

Natural bond orbital analysis 

The Natural bond orbital (NBO) analysis provides structural insight of a conformer by a set of localized bonding, 

anti-bonding, and Rydberg extra valence orbitals [32]. The NBO analysis is a tool used to study delocalization of 

electrons from a lone pair or a filled donor to an unfilled acceptor within the molecule. The second-order Fock-matrix 

is used to calculate the donor–acceptor interactions in the NBO scheme. The interactions cause the delocalization of 

electrons from the occupied orbital to an empty anti-bonding or Rydberg extra valence orbital. For each donor (i) and 

acceptor (j) the delocalization of i → j is determined by the stabilization energy. 

𝐸(2) =  ∆𝐸𝑖𝑗 = 𝑞𝑖
(𝐹𝑖𝑗)

2

(𝐸𝑗−𝐸𝑖)
                                                          (3) 

Here, qi is the occupancy of donor orbital, Ei and Ej are the diagonal elements and Fij is the off diagonal NBO Fock 

matrix element. 

Table 7 shows the results of the NBO analysis of 2-methylimidazole. The large value of E(2) (written as iE(2) in 

the table) suggests strong interaction between electron donor and acceptor, and a greater extent of conjugation of the 

system. From Table 7, it is clear that strong hyper conjugative interactions are formed by orbital overlap between 

LP(N) and π*(C–N), π*(C–C), σ*(C–N), σ*(C–C) with iE(2) values of 201.96, 129.41, 41.25 and 23.47 kJ/mol, 

respectively, between π(C2-N3) and π*(C4–C5) with iE(2) of 90.75 kJ/mol, between π(C4-C5) and π*(C2–N3) with 
iE(2) of 55.69 kJ/mol and between σ (C6-H12) and σ*(C2–N1) orbitals with iE(2) values of 27.11 kJ/mol. These strong 

hyper conjugative interactions result in intra-molecular charge transfer (ICT) leading to the stabilization of the system. 

In the presence of solvent, these orbitals are most likely to be affected and will give rise to the instability or stability of 

the system. 

 

58.00

59.00

60.00

61.00

62.00

63.00

64.00

65.00

66.00

67.00

Water (78.3) DMSO (46.8) n-Octanol (9.9) Chloroform

(4.7)

a
.u

.

Solvents (Dielectric constant)



COMPUTATIONAL STUDY OF GEOMETRY 

97 

 

Table 7. Second Order Perturbation theory analysis of Fock matrix in NBO basis for 2-methylimidazole. 

 

Donor (i) ED/e Acceptor (j) ED/e 
iE(2) 

kJ/mol 

iiE(j)-E(i) 

kJ/mol 

iiiF(ij) 

kJ/mol 

σ(C2-N1) 1.98934 σ*(C5-H9) 0.01275 10.96 3386.90 136.53 

σ(C2-N3) 1.98384 ivRY*(2)C(4) 0.00416 10.17 4883.43 157.53 

π(C2-N3) 1.85698 π*(C4-C5) 0.29818 90.75 840.16 204.79 

σ(C2-C6) 1.98606 
σ*(C4-N3) 0.00975 9.50 3019.33 120.77 

σ*(C5-N1) 0.01340 8.95 2888.05 112.90 

σ(C4-C5) 1.98619 σ*(N1-H7) 0.01725 17.45 3019.33 162.78 

π(C4-C5) 1.87391 π*(C2-N3) 0.37552 55.69 761.40 154.90 

σ(C4-N3) 1.97739 

RY*(2)C(2) 0.00558 10.46 4437.10 152.28 

σ*(C2-C6) 0.02211 31.46 3071.84 220.54 

σ*(C5-H9) 0.01275 14.73 3203.11 154.90 

σ(C5-N1) 1.98522 σ*(C2-C6) 0.02211 17.91 3176.86 168.03 

σ(C5-N1) 1.98522 σ*(C4-H8) 0.01564 14.27 3386.90 154.90 

σ(C6-H10) 1.98086 π*(C2-N3) 0.37552 15.10 1417.77 112.90 

σ(C6-H11) 1.98088 π*(C2-N3) 0.37552 15.06 1417.77 112.90 

σ(C6-H12) 1.98441 σ*(C2-N1) 0.04740 27.11 2546.74 186.41 

LP(1)N(1) 1.59317 

RY*(2) C(5) 0.00230 14.10 3386.90 173.28 

π*(C2-N3) 0.37552 201.96 761.40 280.93 

π*(C4-C5) 0.29818 129.41 787.65 231.04 

LP(1)N(3) 1.92543 

RY*(1) C(2)   0.00943 27.03 3334.39 215.29 

σ*(C2-N1) 0.04740 41.25 2126.66 210.04 

σ*(C4-C5) 0.01960 23.47 2494.23 173.28 
 

iE(2)means energy of hyper conjugative interactions 
iiEnergy difference between donor and acceptor i and j NBO orbital 
iiiF(i,j) is the Fock matrix element between i and j NBO orbitals 
ivRY = Rydberg extra valence orbital 

 

Global reactivity descriptors 

The electrical transport properties of a molecule depend on the energy gap of HOMO and LUMO orbitals. The 

values of the HOMO-LUMO energy gap in various solvents are presented in Table 8 and their trend is shown in Figure 

6. From Figure 6, it is clear that the HOMO-LUMO energy gap decreases on going from polar solvent (Water) to non-

polar solvent (Chloroform). 

 

Table 8. Molecular Orbital Energy (eV) (HOMO and LUMO) of 2-methylimidazole in different solvents with SMD. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Medium (dielectric 

constant) 

Molecular Orbital Energy (eV) 

HOMO LUMO ∆E 

Gas Phase -5.841 0.942 6.783 

Water (78.3) -5.891 1.009 6.900 

DMSO (46.8) -5.883 1.012 6.895 

n-Octanol (9.9) -5.870 1.010 6.880 

Chloroform (4.7) -5.852 1.008 6.860 



SHAHIDUL M. ISLAM ET AL 

98 

 

 
Figure 6. Effect of solvent polarity on the HOMO-LUMO energy gap of 2-methylimidazole. 

 

This suggests that the molecule is stabilized with increasing polarity of the solvent i.e. the molecule is less likely to be 

kinetically reactive, which is in agreement with the calculations of chemical softness. The global chemical reactivity 

descriptors, such as softness, hardness, chemical potential and electrophilicity index, can be calculated from the 

HOMO-LUMO energy gap of a molecule [33-37]. Using Koopman’s theorem for closed-shell molecules, the hardness 

(η), chemical potential (µ), electronegativity (𝝌) and softness (S) are defined as follows: 

 𝜂 =  
𝐼−𝐴

2
                                                                       (4) 

µ =  −
𝐼+𝐴

2
                                                                   (5) 

𝜒 =  
𝐼+𝐴

2
                                                                      (6) 

𝑆 =  
1

𝜂
                                                                       (7) 

where I and A are the ionization potential and electron affinity of the molecule, respectively. The ionization energy and 

electron affinity can be quantified as I = -EHOMO and A = -ELUMO. Parr et al. [36] defined and calculated the global 

electrophilic power of a molecule as electrophilicity index (𝜔) as follows [34]: 

𝜔 =  
µ2

2𝜂
                                                                       (8) 

These new reactivity descriptors can be used to understand the toxicity of various pollutants in terms of their reactivity 

and site selectivity [38-40]. The molecular properties of 2-methylimidazole in different solvent media are presented in 
Table 9. On going from polar to non-polar solvent, the chemical potential, electrophilicity index and electronegativity 

are decreased (Figure 7 and 8). Chemical hardness also decreases on going from polar to non-polar solvent, while the 

opposite relation is found in the case of chemical softness. 

 

Table 9. Effect of solvent polarity on molecular properties of 2-methylimidazole. 

 

Medium (dielectric 

constant) 

Chemical 

hardness (η) 

Softness 

(S) 

Chemical 

potential (µ) 

Electronegativity 

(𝝌) 
Electrophilicity 

index (𝜔) 

Water (78.3) 3.450 0.290 -2.441 2.441 0.863 

DMSO (46.8) 3.447 0.290 -2.435 2.435 0.860 

n-Octanol (9.9) 3.440 0.291 -2.430 2.430 0.858 

Chloroform (4.7) 3.430 0.292 -2.422 2.422 0.855 

 

  

6.840

6.850

6.860

6.870

6.880

6.890

6.900

6.910

Water (78.3) DMSO (46.8) n-Octanol (9.9) Chloroform (4.7)

∆
E

 (
e
V

)

Solvents (Dielectric constant)



COMPUTATIONAL STUDY OF GEOMETRY 

99 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 7. Effect of solvent polarity on the electronegativity of 2-methylimidazole. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 8. Effect of solvent polarity on the electrophilicity index of 2-methylimidazole. 

4. Conclusion 

To understand the structure and reactivity of 2-methylimidazole and related molecules, we have carried out an 

extensive study of the geometry, solvation free energy, dipole moment, molecular electrostatic potential (MESP), 

atomic charge distribution, polarizability, hyperpolarizability, chemical potential, electrophilicity, chemical hardness 

and chemical softnesses of 2-methylimidazole using the B3LYP/6-31G(d,p) level of theory. Geometries obtained from 

B3LYP/6-31G(d,p) are found to be very similar to those obtained from X-ray crystal structure. The solvation free 

energy is highest in the polar aprotic solvent (DMSO) and is lowest in the polar protic solvents (n-octanol and water). 

The dipole moment of 2-methylimidazole increases with increasing polarity of the solvent. Similarly, polarizability and 

hyperpolarizability of 2-methylimidazole also increase with the polarity of the solvent. Molecular electrostatic potential 

(MESP), Mulliken population Analysis (MPA) and Natural population Analysis (NPA) reveal that the most possible 

sites for nucleophilic attack are C2 and H7 and for electrophilic attack are N1 and C4 among the atoms in 2-

methylimidazole. The chemical potential, electrophilicity index and electronegativity increase with the increase of 

solvent polarity. 

 

 

 

0.850

0.852

0.854

0.856

0.858

0.860

0.862

0.864

0.866

Water (78.3) DMSO (46.8) n-Octanol (9.9) Chloroform (4.7)

Solvents (Dielectric constant)

2.410

2.415

2.420

2.425

2.430

2.435

2.440

2.445

Water (78.3) DMSO (46.8) n-Octanol (9.9) Chloroform (4.7)

Solvents (Dielectric constant)



SHAHIDUL M. ISLAM ET AL 

100 

 

5. Acknowledgement 

We would like to thank Dr. John Husband for his helpful suggestions during the preparation of this manuscript. The 

work was carried out by grant DVC/PSR/RD/2016/174 from the Sultan Qaboos University. 

References 

1. Chan, P.C. NTP technical report on the toxicity studies of 2- and 4-Methylimidazole (CAS No. 693-98-1 and 822-
36-6) administered in feed to F344/N rats and B6C3F1 mice. Toxic. Rep. Ser., 2004, 67, 1–G12. 

2.  Mukherjee, A., Kumar, S., Seth, M. and Bhaduri, A.P. Synthesis of 1-methyl-4-nitro-5-substituted imidazole and 

substituted imidazolothiazole derivatives as possible antiparasitic agents. Indian J. Chem., 1989, B28, 391–396. 

3. Norman, S.M., Bennet, R.D., Poling, S.M., Maier, V.P. and Nelson, M.D. Paclobutrazol inhibits abscisic acid 

biosynthesis in Cercospora rosicola. Plant Physiol., 1986, 80, 122–125. 

4. Erera, H., Yeşilela, O.Z., Darcanb, C. and Büyükgüngör, O. Synthesis, spectroscopic, thermal studies, antimicrobial 

activities and crystal structures of Co(II), Ni(II), Cu(II) and Zn(II)-orotate complexes with 2-methylimidazole. 

Polyhedron, 2009, 28, 3087–3093. 

5. Hachula, B., Nowak, M. and Kusz J. Crystal and molecular structure analysis of 2-methylimidazole. J. Chem. 

Crystallogr., 2010, 40, 201–206. 

6. Khabnadideh, S., Rezaei, Z., Khalafi-Nezhad, A., Bahrinajafi, R., Mohamadi, R. and Farrokhroz, A.A. Synthesis of 

N-Alkylated derivatives of imidazole as antibacterial agents. Bioorg. Med. Chem. Lett., 2003, 13, 2863–2865. 

7. Sanders, J.M., Griffin, R.J., Burka, L.T. and Matthews, H.B. Disposition of 2-methylimidazole in rats. J. Toxicol. 

Environ. Health, 1998, A 54,121–132. 

8. Johnson, J.D., Reichelderfer, D., Zutshi, A., Graves, S., Walters, D. and Smith, J. Toxicokinetics of 2-

methylimidazole in male and female F344 rats. Toxicol. Environ. Health, 2002, A 65, 869–879. 

9. Chan, P.C., Sills, R.C., Kissling, G.E., Nyska, A. and Richter, W. Induction of thyroid and liver tumors by chronic 

exposure to 2-methylimidazole in F344/N rats and B6C3F1 mice. Arch. Toxicol., 2008, 6, 399–412. 

10. Moore-Testa, P., Saint-Jalm, Y. and Testa A. Identification and determination of imidazole derivatives in cigarette 

smoke. J. Chromatogr., 1984, 290, 263–274. 

11. Wilkinson, C.F. and Hetnarski, K. Structure-activity relationships in the effects of 1-alkylimidazoles on 

microsomal oxidation in vitro and in vivo. Biochem. Pharmacol., 1974, 23, 2377–2386. 

12. Jimenez, P., Roux, M.V. and Turrion, C. Thermochemical properties of N-heterocyclic compounds IV. Enthalpies 

of combustion, vapour pressures and enthalpies of sublimation, and enthalpies of formation of 2-methylimidazole 

and 2-ethylimidazole. J. Chem. Thermodynamics, 1992, 24, 1145-1149. 

13. Yu, X.Y., Cai, S.H., Xu, X. and Chen, Z. NMR and theoretical study on the coordination and solution structures of 

the Interaction between diperoxovanadate complexes and histidine-like ligands. Inorg. Chem., 2005, 44, 6755-62. 

14. Hernández-Marín, E. and Lemus-Santana, A.A. Theoretical study of the formation of complexes between CO2 and 

nitrogen heterocycles. J. Mex. Chem. Soc., 2015, 59, 36-42. 

15. Anbarasan, P.M., Kumar, P.S., Geetha, M., Govindan, R., Manimegalai, S. and Velmurugan, K. Geometries, 

electronic structures and electronic absorption spectra of silicon dichloride substituted phthalocyanine for dye 

sensitized solar cells. Rec. Res. Sci. Tech., 2010, 2, 8–16. 

16. Praveen, P.L. and Ojha, D.P. Substituent and solvent effects on UV–visible absorption spectra of liquid crystalline 

disubstituted biphenylcyclohexane derivatives– a computational approach. Cryst. Res. Technol., 2012, 47, 91–100. 

17. Targema, M., Obi-Egbedi, N.O. and Adeoye, M.D. Molecular structure and solvent effects on the dipole moments 

and polarizabilities of some aniline derivatives. Computational and Theoretical Chemistry, 2013, 1012, 47–53. 

18. Jayaprakash, A., Arjunan, V., Jose, S.P. and Mohan, S. Vibrational and electronic investigations, thermodynamic 

parameters, HOMO and LUMO analysis on crotonaldehyde by ab initio and DFT methods. Spectrochimica Acta 

Part A, 20100, 83, 411– 419. 

19. Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M.A., Cheeseman, J.R., Scalmani, G., Barone, 

V., Mennucci, B. G., Petersson, A., Nakatsuji, H., Caricato, M., Li, X., Hratchian, H.P., Izmaylov, A.F., Bloino, J., 

Zheng, G., Sonnenberg, J.L., Hada, M., Ehara, Toyota, M. K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., 

Honda, Y., Kitao, O., Nakai, H., Vreven, T., Montgomery Jr., J.A., Peralta, J.E., Ogliaro, F., Bearpark, M., Heyd, 

J.J., Brothers, E., Kudin, K.N., Staroverov, V.N., Kobayashi, R., Normand, J., Raghavachari, Rendell, K. A., 

Burant, J.C., Iyengar, S.S., Tomasi, J.,   Cossi, M., Rega, N., Millam, J.M., Klene, M., Knox, J.E., Cross, J.B., 

Bakken, V., Adamo, C., Jaramillo, J., Gomperts, R., Stratmann, R.E., Yazyev, O., Austin, A.J., Cammi, R., 

Pomelli, C., Ochterski, J.W., Martin, R.L., Morokuma, K., Zakrzewski, V.G., Voth, G.A., Salvador, P., 

Dannenberg, J.J., Dapprich, S., Daniels, A.D., Farkas,O., Foresman, J.B., Ortiz, J.V., Cioslowski,  J. and Fox, D.J. 

Gaussian 09, Revision A.02, Gaussian, Inc., Wallingford, CT, 2009. 

20.  Islam, S.M., Huelin, S.D., Dawe, M. and Poirier, R.A. Comparison of the standard 6-31G and binning-curtiss basis 

sets for third row elements. J. Chem. Theory. Comput., 2008, 4, 86-100. 

21. Llano, J. and Eriksson, L.A. Mechanism of hydroxyl radical addition to imidazole and subsequent water 

elimination. J. Phys. Chem. B, 1999, 103, 5598-5607. 



COMPUTATIONAL STUDY OF GEOMETRY 

101 

 

22. Becke, A.D. Density-functional thermochemistry. III. The role of exact exchange.  J. Chem. Phys., 1993, 98, 5648-

5652. 

23. Lee, C., Yang, W. and Parr, R.G. Development of the Colle-Salvetti correlation-energy formula into a functional of 

the electron density. Phys. Rev. B, 1988, 37, 785-789. 

24. Stephens, P.J., Devlin, F.J., Chabalowski, C.F. and Frisch, M.J. Ab Initio Calculation of Vibrational Absorption 

and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem., 1994, 98, 11623-11627. 

25. Cramer, C.J. Essential of computational chemistry. Second edition, Wiley, England, 2004. 

26. Marenich, A.V., Cramer, C.J. and Truhlar, D.G. Universal solvation model based on solute electron density and on 

a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. J. Phys. 

Chem. B, 2009, 113, 6378–6396. 

27. Suhasini, M., Sailatha, E., Gunasekaran, S. and Ramkuma, G.R. Vibrational and electronic investigations, 

thermodynamic parameters, HOMO and LUMO analysis on Lornoxicam by Density Functional Theory. J. 

Molecular Structure, 2015, 1100, 116–128. 

28. Govindarajan, M., Karabacak, M., Periandy, S. and Xavier, S. Vibrational spectroscopic studies, NLO, HOMO–

LUMO and electronic structure calculations of α,α,α-trichlorotoluene using HF and DFT. SpectrochimicaActa 

Part A: Molecular and Biomolecular Spectroscopy, 2012, 94, 53–64. 

29. Munoz-Caro, C., Niño, A., Senent, M.L., Leal, J.M. and Ibeas, S. Modeling of protonation processes in 

acetohydroxamic acid. J. Org. Chem., 2000, 65, 405–410. 

30. Santamaria, R., Cocho, G., Corona, L. and González, E. Molecular electrostatic potentials and Mulliken charge 

populations of DNA mini-sequences. Chemical Physics, 1998, 227, 317–329. 

31.  Kleinman, D.A. Nonlinear Dielectric Polarization in Optical Media. Phys. Rev., 1962, 126, 1977. 

32. Shunmugam, R. and Sathyanarayana, D. Raman and polarized infrared spectra of pyridine-2-thione. 

Spectrochim.Acta A, 1984, 40, 757-761. 

33. Parr, R.G., Donnelly, R.A., Levy, M. and Palke, W.E. Electronegativity: The density functional viewpoint. J. 

Chem. Phys., 1978, 68, 3801–3807. 

34.  Parr, R.G. and Pearson, R.G. Absolute hardness: companion parameter to absolute electronegativity. J. Am. Chem. 

Soc., 1983, 105, 7512–7516. 

35.  Parr, R.G. and Chattraj, P.K. Principle of maximum hardness. J. Am. Chem. Soc., 1991, 113, 1854–1855. 

36.  Parr, R.G., Szentpály, L.V. and Liu, S. Electrophilicity index. J. Am. Chem. Soc., 1999, 121, 1922–1924. 

37.  Chattaraj, P.K., Maiti, B. and Sarkar, U. Philicity: A unified treatment of chemical reactivity and selectivity. J. 

Phys. Chem. A., 2003, 107, 4973–4975. 

38. Parthasarathi, R., Padmanabhan, J., Subramanian, V., Sarkar, U., Maiti, B. and Chattaraj, P. Toxicity analysis of 

benzidine through chemical reactivity and selectivity profiles: A DFT Approach. Int. Electron. J. Mol. Des., 2003, 

2, 798–813. 

39. Parthasarathi, R., Padmanabhan, J., Subramanian, V., Sarkar, U., Maiti, B. and Chattaraj, P. Intermolecular 

reactivity through the generalized philicity concept. Chem. Phys. Lett., 2004, 394, 225–230. 

40. Parthasarathi, R., Padmanabhan, J., Subramanian, V., Sarkar, U., Maiti, B. and Chattaraj, P. Toxicity analysis of 

33'44'5-pentachloro biphenyl through chemical reactivity and selectivity profiles. Curr. Sci., 2004, 86, 535–542. 

 

 

Received   22 March 2016        

Accepted   22 September 2016